Air, oil or—for transformers with superconducting windings composed of high-temperature superconductor material (HTSL)—liquefied gases are used for forced cooling of the windings and of the core, which carries the magnetic flux, in transformers. In order to design the cooling to be as effective as possible, a flow path is normally specified for the coolant within the scaled tank which holds the core and the upper and lower voltage windings which are in each case associated with one another concentrically. In a known transformer of this type, the upper and lower voltage windings which are in each case associated with one another concentrically are arranged in annular, pocket-like chambers, which are open at the top and thus towards the rest of the tank volume. A further chamber, which is annular but is designed to be flat, is arranged underneath these pocket-like chambers and is provided with through-openings to the pocket-like chambers. Fresh coolant flows via an inlet into the flat chamber, where it is distributed into the pocket-like chambers, rises in them, and then flows into the rest of the interior of the tank before leaving the tank via an outlet. In this way, the coolant absorbs heat first of all from the windings and then from the magnetic core and the wall of the tank, and finally from the current feeders and winding connections. The walls of the chambers and the surfaces of the core and of the tank in this case form guide surfaces for guiding the coolant (U.S. Pat No. 4,424,502 A1).